Working out perimeters 0 Overview Using this Resource Connecting to the Curriculum Marking Student Responses Working with Students Further Resources This task is about using algebraic expressions to find lengths of a shape. Question 2Change answer a) Write an expression, in its simplest form, for the length of a) Write an expression, in its simplest form, for the length of i) side Q: ii) side R: Question 2Change answer b) i) Write an expression that would allow you to find the length of the perimeter around the shape. b) i) Write an expression that would allow you to find the length of the perimeter around the shape. Question 2Change answer ii) Simplify your expression. ii) Simplify your expression. Question 2Change answer c) Use your expression in b) ii) to find the value of x for a perimater of 104cm. Show all your working in your calculation. c) Use your expression in b) ii) to find the value of x for a perimater of 104cm. Show all your working in your calculation. Task administration: This task is completed with pencil and paper or online. Level: 5 Curriculum info: Maths, Number and Algebra, Equations and expressions Keywords: algebraic expressions, simplify, perimeter, linear equations Description of task: Students evaluate and simplify algebraic expressions for the side lengths and perimeter of a composite shape. They then find x for a given perimeter. Learning Progression FrameworksThis resource can provide evidence of learning associated with Using symbols and expressions to think mathematically, sets 6-7 within the Mathematics Learning Progressions Frameworks.Read more about the Learning Progressions Frameworks. Answers/responses: Y10 (08/2001) a) i) ii) x - 1 x - 2 difficult difficult b) i) Any 1 of (2 marks - difficult): 2(2x - 1) + 2(3x - 2) 3x - 2 + 2x - 1 + x - 2 + x + 2x + x - 1 3x - 2 + 2x - 1 + 2x + x + answer to a) i) + answer to a) ii) Other possible answers. or Any 1 of (1 mark - moderate): 3x - 2 + 2x -^{-} 1 + 2x + x + Q + R 8x - 3 + Q + R b) ii) Any 1 of (1 mark - moderate): 10x - 6 2(5x - 3) 2(3x - 2) + 2(2x - 1) if not already given in b) i) Answer to b) i) simplified correctly. NOTE: Give both marks if simplification only is given. c) Any 1 of (2 marks - very difficult): 11, e.g., working 104 = 10x - 6 110 = 10x 104 = answer to b) ii) which is then solved correctly. Correct substitution into b)ii) but incorrect calculation (1 mark - difficult). Diagnostic and formative information: Common error Likely calculation Likely misconception a) i) ii) (2x - 1) - x (3x - 2) - 2x Expression not written in its simplest form. b) i) 2(3x - 2) + 2(2x - 1) - (2x + x) 2(3x - 2 + 2x - 1) - 2(2x + x) Confusion in calculating perimeter with area. c) 9.8 10x - 6 = 104 \ 10x = 98 Solving equation incorrectly, subtracting instead of adding 6 to the right-hand side. Length, area and algebra